Error correcting codes for future storage with distributed nature

Abstract

In this thesis, error correcting codes for future storage with distributed nature are suggested and theoretically analyzed. For not only traditional storage systems like hard-disk-drive (HDD) and solid-state-drive (SSD) but also recent massive cloud system, error-correcting codes with distributed nature are promising for achieving dynamic system performance targets. In this thesis, three different error-correcting codes with distributed nature are proposed for various types of storage systems. In Chapter 2, two-dimensional (2D) cyclic codes are proposed which correct any single occurrence of known 2D error patterns. First, the code construction procedure begins with designing 2D code theoretically to have distinct syndrome sets for all target 2D patterns. After that, syndrome set for each pattern is further designed to have distinct elements for all possible pattern locations. In Chapter 3, practical concatenated coding scheme with multiple short component polar codes and single-parity-check codes is proposed. As for hardware-complexity, required memory is significantly reduced by utilizing small decoding unit geared to serial decoding of short component polar codes. In theoretic analysis, each short component polar code shows much improved error-rate scaling-behavior thanks to simple single-parity-check decoding, i.e., the error rate decays as fast as a long single polar code along with overall code-length while retaining considerable memory advantage. In the last chapter, storage-repair bandwidth trade-off for distributed storage system with knowledge of coding connectivity is analyzed. Conventional distributed storage system is based on repair of failures with randomly chosen $d$-helper nodes and random linear network coding. If the repair process of a failed node is based on knowledge of local connections, failure can be repaired by the connected helper nodes only. Information flow analysis of sparsely-coded distributed storage system is presented in numerical sense. Through the approach, improved storage-repair bandwidth pair is obtained with much less helper nodes.